# Normal approximation for the proportion P hat

• ChrisBlack

## Homework Statement

68% of students favor a new policy, we are interested in the proportion of 45 students in a math class who favor the same policy.

What is the probability that the proportion of the class that favors the policy is no more than two-thirds?

## The Attempt at a Solution

I found the mean, .68, and the standard deviation, .047. I don't know where to take it from here though

## Homework Statement

68% of students favor a new policy, we are interested in the proportion of 45 students in a math class who favor the same policy.

What is the probability that the proportion of the class that favors the policy is no more than two-thirds?

## The Attempt at a Solution

I found the mean, .68, and the standard deviation, .047. I don't know where to take it from here though

If the proportion of the class in favor is no more than 2/3, what does that say about the _number_ of students in favor? What is the probability distribution of the number (out of 45) who are in favor? Note: the number in favor can be 0 or 1 or 2 or ... or 45; I am asking you to describe a formula for the probability that k students are in favor, for any of the 46 values of k. What are the mean and standard deviation of the number in favor?

Once you have dealt with these questions you will be in a better position to know what to do next.

RGV

So no more than 30 students can favor it. This does not sound like anything I have done in class so far, does it have to do anything with the fact that 68% of the data falls within 2 standard deviations of the mean?

So no more than 30 students can favor it. This does not sound like anything I have done in class so far, does it have to do anything with the fact that 68% of the data falls within 2 standard deviations of the mean?

I don't know what you have done so far, so that is why I asked the questions in my previous post. Do you know the distribution of the number if favor? Maybe you do, without even realizing it. Let's work through it slowly. Instead of asking about the number of students in 45 that are in favor, suppose instead I asked about tossing coins or dice. In fact, suppose I have a biased coin, with probability p = 0.68 of falling 'heads' in each toss. I toss it 45 times and count the resulting number of 'heads'. Do you agree this is the same problem? Have you seen before the distribution of the number of 'heads' in coin tossing?